Design Strategies for Sparse Control Of Random Time-Varying NETWORKS

This paper considers the design of sparse controllers for driving dynamics defined over a network of agents whose connectivity changes randomly over time. This scenario is of interest when the underlying topology is affected by random link failures such as communication drops in sensor networks. To account for the randomness in the topology, it relies on the recent concept of controllability in the mean that aims driving the expected dynamic to the target state, while minimizing second-order statistical distances. We show that by departing from the conventional minimal energy solution, it is possible to recast the sparse control design problem as a semi-definite programming and use convex solvers to obtain a sparse solution. Moreover, these findings enrich the state-of-the-art design methods with design strategies that do not necessarily rely on the graph smoothness for the target state. The effectiveness of the proposed findings is corroborated with numerical results in Erdös-Réinyi and k-nearest neighbors graphs.